簡約 100e^{-0.005*2}

解

簡約

100 e^{- 0.005 \cdot 2}

99.00498 \dots

解答ステップ

100 e^{- 0.005 \cdot 2}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

= 100 \cdot \frac{1}{e ^{2 \cdot 0.005}}

数を乗じる:

0.005 \cdot 2 = 0.01

= 100 \cdot \frac{1}{e ^{0.01}}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 100}{e ^{0.01}}

数を乗じる:

1 \cdot 100 = 100

= \frac{100}{e ^{0.01}}

e^{0.01} = 1.01005 \dots

= \frac{100}{1.01005 \dots}

数を割る:

\frac{100}{1.01005 \dots} = 99.00498 \dots

= 99.00498 \dots